Pearce_09
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Hello,
(**under addition** not multiplication)
in my question I am trying to prove that "the set of all integers (Z)" mapped to "the set of all rational numbers (Q)" is isomorphic
ie. Z --> Q
through out my work I have shown that yes it is injective, and it is a homomorphism, but I have not shown it is or isn't surjective.
I think that it is not surjective, bucause the cardnality of Z is less than the cardnality of Q.
ie. |Q| > |Z| (the set Q is much bigger than the set Z)
so my question to you is, am i correct? and if you feel different about this, please explain to me what you think.
thank you
adam
(**under addition** not multiplication)
in my question I am trying to prove that "the set of all integers (Z)" mapped to "the set of all rational numbers (Q)" is isomorphic
ie. Z --> Q
through out my work I have shown that yes it is injective, and it is a homomorphism, but I have not shown it is or isn't surjective.
I think that it is not surjective, bucause the cardnality of Z is less than the cardnality of Q.
ie. |Q| > |Z| (the set Q is much bigger than the set Z)
so my question to you is, am i correct? and if you feel different about this, please explain to me what you think.
thank you
adam